Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.
Bismut,The atiyah-singer index theorem for families of dirac operators,Invent
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Dai-Freed anomalies and level matching in heterotic asymmetric orbifolds
Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.